Calculus and Quantum Mechanics

The usefulness of calculus is limited to Classical Mechanics. Classical mechanics deals with mass that is “centered” and with waves that are “spread out.” In both cases, physical locations may be assumed to be uniform in their characteristics and to be distributed uniformly as points in space.

This assumption no longer holds in the subatomic region, which is the concern of quantum mechanics. In this region, the inertia (state of motion) starts to transition from “mass of particles” to “frequency of waves.” With this transition the nature of locations starts to change from “centered” to being “spread out.”

Thus the locations in the atomic region cannot be considered to be uniform, and they cannot be treated by the infinitesimals of calculus with any certainty.

Calculus cannot be applied with any certainty to the problems of Quantum Mechanics in the subatomic region.

Comments

V:” In this region, the inertia (state of motion) starts to transition from “mass of particles” to “frequency of waves.” ”

This is an unfounded assertion based on your earlier incorrect assumption that you could directly equate frequency to mass with your assumption of
E = hf and E = mc^2 implying hf = mc^2. Nope. You’ve got to get the idea of angular momentum as it relates to the energy of the wave. Its effect is directly observed in Compton scattering. It can’t be ignored. It’s very much like the difference between a bowling ball simply rolled down the lane and a ball that has spin put into it as well. At the impact point very different energy distribution patterns occur making it possible for an observer to distinguish between a rolled ball and a spun ball.

Also, I see no reason why calculus would not be able to describe quantum states. Calculus is a mathematics of change. That is all. As long as the changes at the quantum level are continuous within a domain, then calculus can describe the changes within that domain.

I believe it would greatly help your understanding of quantum phenomena if you were able to properly grasp the concept of “root of -1”.

To not do so leaves you in a condition of being “physical-centric” i.e. having to have a matter, energy, 3-space and time explanation of things.

The math of quantum mechanics – as we saw back in the Schrodinger discussion – requires the inclusion of the “imaginary” operator. It can’t be ignored, either.

The forward and oscillatory motion of a photon may be visualized as a corkscrew motion. As frequency increases the translation decreases, and the threads of this motion seems to come closer together. Ultimately, that corkscrew motion of frequency transforms into spinning motion of mass.

It is going good. Of course, I am creating my own concepts, which are different from the concepts being taught.

In fact, nothing much exists in Quantum Mechanics in terms of concepts. It is just mathematics. The mathematical concept that it is based on is that space is a set of points and a point determines a location. So, it is calculating the probability of a point location even when there is no such thing in actuality.